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When 1 + 1 = 5: Dyscalculia and Working Memory

Jacob's mother writes that ‘Jacob, 10-years-old, still struggles with number bonds to 10. Learning to tell the time is still slow - he has not mastered half-past. Although he managed to learn his 5x tables because we practiced all summer, this has now gone'.

Jacob has dyscalculia, a math disability where students struggle to learn or understand mathematics. Students with dyscalculia find it difficult to decipher math symbols (e.g. +, -), counting principles (‘two' stands for 2), solving arithmetic problems, and usually transpose numbers (e.g. 75 becomes 57). However, dyscalculia encompasses more than problems with numbers - there is also a struggle with telling the time as in Jacob's case, identifying left from right, and recognizing patterns.

But why do some students struggle to learn numbers and certain mathematical principles?

Working Memory plays a key role. To solve a mathematical problem like 1 + 1, we need to use our Visuo-Spatial Working Memory. Visuo-spatial working memory functions like a big mental blackboard that gives us a space to write all of the numbers necessary to solve a problem. It also works together with the brain's calculator known as the Intraparietal Sulcus (IPS), located in the right hemisphere. Brain imaging studies that looked at brain activity while people were counting and calculating quantities reveal that when we count, regardless of whether it is shapes, numbers, or objects, the IPS is activated. In dyscalculics, this area underperforms and may underpin their maths difficulties.

Like Jacob, the student with dyscalculia has clear working memory deficits. However, the link between working memory and math skills depends on the age of the child as well as the type of math task. Verbal working memory plays a strong role in math skills in seven-year-olds and is a reliable indicator of dyscalculia in the first year of formal schooling. Once children reach adolescence, verbal working memory is no longer significantly linked to mathematical skills. One explanation for this change is that verbal working memory plays a crucial role for basic arithmetic skills like learning arithmetic rules and retaining relevant data such as carried digits when they are young. However, as children get older other factors such as number knowledge and strategies play a greater role.

If you are working with a student with dyscalculia, it is important not only to address their difficulties with numbers, but to also assess their Working Memory. It is possible that they have a small mental blackboard (visuo-spatial Working Memory) that is making it harder for them to apply their number knowledge in a classroom situation.

We assume that because a child shows no particular aptitude for arithmetic in the early years, then he/she has no particular talent for mathematics, and once dumped in a low maths set, well, you're there for life, baby. You are right that the nature of the skill required to be good at maths changes, especially once any form of higher maths starts to be introduced. Unfortunately for the child whose arithmetic left a lot to be desired early on, he/she may never be introduced to the higher maths topics where he/she might really blossom in the subject.

I don't know if this has to do with dyscalculia or working memory, but I can imagine that persuading Mrs. Higginbottom that Little Johnny who can't calculate for toffee might in fact be a gifted mathematician, given a chance, would be an uphill struggle.

There's no greater waste than a wasted intellect, and I prefer to err on the side of giving people a chance.

Thanks for your comment. It is possible that a child is having difficulty learning math (or 'shows no aptitutde' as you phrase it), because their Working Memory space is not big enough to take in all the information. While their peers may do fine with 3 pieces of information, they may be struggling to keep in mind just 1 or 2 things the teacher is saying. You are right that working memory problems do not represent a developmental lag--a student won't be able to 'catch up' over time. However, with early diagnosis we can provide effective support and training to foster learning.

Your article caught my eye today and I found I really enjoyed reading it (not in a mean way, I see how this can be terribly fustrating for a child). I'm sure not many people know this exist and I'm glad you educated me more upon the subject. So, yeah thank you.